{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3DFVSLIOEG4O2UJKYCYGH2O6MN","short_pith_number":"pith:3DFVSLIO","canonical_record":{"source":{"id":"1610.08255","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-26T09:44:49Z","cross_cats_sorted":[],"title_canon_sha256":"761b500e1f83ebcf8fa6a13099c3049dd53efc1d561b846fc9f9de7d5208e495","abstract_canon_sha256":"f41788b017daf2819b91c234c0ed57bd559a8684be3cd7c4a54bd4ed4e417236"},"schema_version":"1.0"},"canonical_sha256":"d8cb592d0e21b8ed512ac0b063e9de63698754f0609337ca16aa08a3614fc883","source":{"kind":"arxiv","id":"1610.08255","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08255","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08255v3","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08255","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"pith_short_12","alias_value":"3DFVSLIOEG4O","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3DFVSLIOEG4O2UJK","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3DFVSLIO","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3DFVSLIOEG4O2UJKYCYGH2O6MN","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08255","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-26T09:44:49Z","cross_cats_sorted":[],"title_canon_sha256":"761b500e1f83ebcf8fa6a13099c3049dd53efc1d561b846fc9f9de7d5208e495","abstract_canon_sha256":"f41788b017daf2819b91c234c0ed57bd559a8684be3cd7c4a54bd4ed4e417236"},"schema_version":"1.0"},"canonical_sha256":"d8cb592d0e21b8ed512ac0b063e9de63698754f0609337ca16aa08a3614fc883","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:05.224407Z","signature_b64":"ZBcLl53EWZH6KwkhclqsB6uiyd5ZbATxJSzApCP+1KEblCNm2MJdkfX4AB4CuGKqtPUkgvOkRjDu9h6+1T9oAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8cb592d0e21b8ed512ac0b063e9de63698754f0609337ca16aa08a3614fc883","last_reissued_at":"2026-05-18T01:00:05.223936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:05.223936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08255","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t1P6geQyGe+bmWXLcJYlsXz4Db2KDyu5IZXEpzry4xD3GIqgTPYiq7F9LPcF00eiUlsRw1/rqQaD9vYN3+xbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T03:00:51.349547Z"},"content_sha256":"d562a3a2df45a27242ac0a5daa670403fe44d73fb4738401aafe26ca65b59cd6","schema_version":"1.0","event_id":"sha256:d562a3a2df45a27242ac0a5daa670403fe44d73fb4738401aafe26ca65b59cd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3DFVSLIOEG4O2UJKYCYGH2O6MN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Biderivations of W-algebra $W(2,2)$ and Virasoro algebra without skewsymmetric condition and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Xiaomin Tang","submitted_at":"2016-10-26T09:44:49Z","abstract_excerpt":"In this paper, we characterize the biderivations of W-algebra $W(2,2)$ and Virasoro algebra $Vir$ without skewsymmetric condition. We get two classes of non-inner biderivations. As applications, we also get the forms of linear commuting maps on W-algebra $W(2,2)$ and Virasoro algebra $Vir$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08255","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:00:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WybTBqvq2k5n7SNYjOuZ3RWdpusoer/Ms0cQLLsra9P/MjxPeBnuLy1/xtD+rZzA/9JO3kvRwHqQfmOiYn7eAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T03:00:51.349892Z"},"content_sha256":"095be0ebaa009ac738f9f6371bf8b28e25e97423ba7530325812579487063158","schema_version":"1.0","event_id":"sha256:095be0ebaa009ac738f9f6371bf8b28e25e97423ba7530325812579487063158"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DFVSLIOEG4O2UJKYCYGH2O6MN/bundle.json","state_url":"https://pith.science/pith/3DFVSLIOEG4O2UJKYCYGH2O6MN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DFVSLIOEG4O2UJKYCYGH2O6MN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T03:00:51Z","links":{"resolver":"https://pith.science/pith/3DFVSLIOEG4O2UJKYCYGH2O6MN","bundle":"https://pith.science/pith/3DFVSLIOEG4O2UJKYCYGH2O6MN/bundle.json","state":"https://pith.science/pith/3DFVSLIOEG4O2UJKYCYGH2O6MN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DFVSLIOEG4O2UJKYCYGH2O6MN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3DFVSLIOEG4O2UJKYCYGH2O6MN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f41788b017daf2819b91c234c0ed57bd559a8684be3cd7c4a54bd4ed4e417236","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-26T09:44:49Z","title_canon_sha256":"761b500e1f83ebcf8fa6a13099c3049dd53efc1d561b846fc9f9de7d5208e495"},"schema_version":"1.0","source":{"id":"1610.08255","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08255","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08255v3","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08255","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"pith_short_12","alias_value":"3DFVSLIOEG4O","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3DFVSLIOEG4O2UJK","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3DFVSLIO","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:095be0ebaa009ac738f9f6371bf8b28e25e97423ba7530325812579487063158","target":"graph","created_at":"2026-05-18T01:00:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we characterize the biderivations of W-algebra $W(2,2)$ and Virasoro algebra $Vir$ without skewsymmetric condition. We get two classes of non-inner biderivations. As applications, we also get the forms of linear commuting maps on W-algebra $W(2,2)$ and Virasoro algebra $Vir$.","authors_text":"Xiaomin Tang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-26T09:44:49Z","title":"Biderivations of W-algebra $W(2,2)$ and Virasoro algebra without skewsymmetric condition and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08255","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d562a3a2df45a27242ac0a5daa670403fe44d73fb4738401aafe26ca65b59cd6","target":"record","created_at":"2026-05-18T01:00:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f41788b017daf2819b91c234c0ed57bd559a8684be3cd7c4a54bd4ed4e417236","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-10-26T09:44:49Z","title_canon_sha256":"761b500e1f83ebcf8fa6a13099c3049dd53efc1d561b846fc9f9de7d5208e495"},"schema_version":"1.0","source":{"id":"1610.08255","kind":"arxiv","version":3}},"canonical_sha256":"d8cb592d0e21b8ed512ac0b063e9de63698754f0609337ca16aa08a3614fc883","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8cb592d0e21b8ed512ac0b063e9de63698754f0609337ca16aa08a3614fc883","first_computed_at":"2026-05-18T01:00:05.223936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:05.223936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZBcLl53EWZH6KwkhclqsB6uiyd5ZbATxJSzApCP+1KEblCNm2MJdkfX4AB4CuGKqtPUkgvOkRjDu9h6+1T9oAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:05.224407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08255","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d562a3a2df45a27242ac0a5daa670403fe44d73fb4738401aafe26ca65b59cd6","sha256:095be0ebaa009ac738f9f6371bf8b28e25e97423ba7530325812579487063158"],"state_sha256":"871b5540e4a254453f7b3e245f821467e329c87b970d696521d5b14bd89f1762"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RF5b4sIcC5MrgyQg7N/9cPwmifovGaEuOQjluC6xgZSu7nNIHO+uGMvyQcA/B4lvD1OrkiEqS/Fc1qZv3iZaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T03:00:51.351973Z","bundle_sha256":"00b4e23103f1a948d4f6c186f08458ea958a8d69d65f05da02c5ace7ae122892"}}